Economics
Dominant Strategy
A dominant strategy in economics refers to a choice that yields the highest payoff for a player regardless of the choices made by other players. It is a strategy that is always the best option, regardless of the actions of other players. In game theory, identifying dominant strategies helps to predict the most rational choices for players in strategic interactions.
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4 Key excerpts on "Dominant Strategy"
- Thomas J. Webster(Author)
- 2018(Publication Date)
- Routledge(Publisher)
A player with a Dominant Strategy should not be concerned with a rival’s behavior. The only thing that matters is selecting a strategy that always results in the best payoff. This leads us to our first general principle for playing noncooperative games: Principle: A rational player should adopt a Dominant Strategy whenever possible. Alternatively, a rational player should not adopt a dominated strategy. We also observed that for a game to have a unique Nash equilibrium it is only necessary for one player to have a Dominant Strategy. The reason for this is that the player without a Dominant Strategy will predict that a rational rival will adopt a Dominant Strategy and adopt the best strategy in response. This brings us to our second general principle: Principle: A rational player believes that a rational rival will always adopt a dominant strat-egy and avoid a dominated strategy whenever possible, and will act on that belief. Moreover, a player believes that rivals think the same way, and will also act on their beliefs. ITERATED ELIMINATION OF STRICTLY DOMINATED STRATEGIES So far, we have considered noncooperative, simultaneous-move, one-time games involving two players with just two strategies to choose from. Suppose, however, that two players in a game are required to select from among three or more strategies. In games where both players have a strictly Dominant Strategy, finding the Nash equilibrium is straightforward. On the other hand, suppose that neither player has a strictly Dominant Strategy. Is it still possible for a two-player, multistrategy game to have a unique Nash equilibrium? To answer this question, consider the version of the oil-drilling game depicted in Figure 2.6. The payoff matrix for this static game introduces a third strategy— don’t drill. The reader should verify that neither PETROX nor GLOMAR has a strictly Dominant Strategy. Which strategy should both companies adopt? Let us consider the problem from GLOMAR’s perspective.
- John Hoag(Author)
- 2007(Publication Date)
- WSPC(Publisher)
A similar definition holds for Player 2. Remark A dominated strategy is one that is worse than another strategy no matter what the other player does. So if no matter what strategy the other player plays, I am always worse off playing s k than s j , s j dominates s k , and I would never play s k . It can be shown that if only one strategy is left for each player after all dominated strategies are removed, then the remaining pair of strategies, one for each player, is a Nash equilibrium. It is important to note that it is possible that a Nash equi-librium may exist even when dominated strategies are not present. Thus we cannot depend on using dominated strate-gies as the only device to discover a Nash equilibrium. Note that if we could always find an equilibrium from dominant strategies alone, we would violate the view of games that Von Neumann held, that we might not know what the other person intends to do. When we can find a Nash equilibrium by elim-inating dominated strategies, this view of Von Neumann’s is not true — we do know what the other person intends to do. But can we always find a Nash equilibrium? Exercise 3 Compute the best reply functions for each consumer in the following game. What do you find for equilibria in this case? 2 1 L C R Best reply T (2, 2) (1, 1) (3, 4) M ( − 1, 3) ( − 1, − 2) ( − 2, 1) B (4, 3) (0, 0) ( − 1, − 2) Best reply Game Theory 279 Remark The problem faced here is that more than one equilibrium may occur. What do we do then? And notice that here we cannot always decide whether one of the equilibria is “bet-ter” than the other. In some cases, as in this case, it may be that one of the equilibria is clearly better for both players than another equilibrium. In that case, it may be that if the game is played over and over, some convention arises to increase the probability that the players will play the proper strategy to achieve the most desired outcome.
eBook - PDF- Rhona C. Free(Author)
- 2010(Publication Date)
- SAGE Publications, Inc(Publisher)
18 ECONOMICS OF STRATEGY QUAN WEN Vanderbilt University E conomic and other rational decision making involves choosing one of the available actions for the environ-ment that the decision maker is facing, given his or her objectives. Rational decision making and the subsequent choice of action depend on these two primary factors. Economics of strategy is concerned with how a rational deci-sion maker's behavior in choosing an action can be explained by logical and strategic reasoning. A simple decision problem can be viewed as the simplest strategic problem, when there is only one agent for a given environment. Many economic problems, however, involve multiple decision makers. Our primary goal in economics of strategy is to provide a system-atic analysis of how each decision maker behaves and how the strategic logics of the decision makers interact. The primary tool researchers use in strategic analysis is game theory. Game theory provides us with a systematic and logical method for studying decision-making problems that involve multiple decision makers. Game theory has been applied in many areas of economic studies, such as industrial organization and strategic international trade. Application of game theory has different implications, depending on the specific economic environment. To facilitate our understand-ing of how rational and strategic decisions are made, we focus on firms' strategic behavior in settings with different market structures. We review necessary and commonly used concepts and modeling techniques of game theory and apply them in analyzing firms' strategic behavior. Competitive Market and Competitive Firms We usually do not think that an individual firm behaves strategically in a competitive market; after all, a competitive firm simply chooses a feasible action to maximize its profit. However, a competitive firm's decision problem can be viewed as a strategic problem with only one agent.
eBook - PDFYour Career Game
How Game Theory Can Help You Achieve Your Professional Goals
- Nathan Bennett, Stephen A. MIles(Authors)
- 2010(Publication Date)
- Stanford Business Books(Publisher)
For this reason, players are advised to adopt a mixed strategy (that is, randomly choosing between rock, paper, and scissors) 36 chapter two in order to keep the other player guessing. Players who adopt a pure strat-egy (such as selecting “rock” every time or moving predictably from paper to scissors to rock) quickly become transparent, and their strategies are easily rendered ineffective. And, Kasporov notes that “when your opponent can eas-ily anticipate every move you make, your strategy deteriorates and becomes commoditized.” Dominant and Dominated Strategies A Dominant Strategy is one that is always best for a player to implement; a dominated strategy is one that can be overcome by an opponent. A strategy is considered dominant if it provides the best return to the player, regardless of the strategies employed by other players. Logically, then, a dominated strategy is one that provides a poor return to the player, regardless of the strategies employed by other players. There is no Dominant Strategy in the Rock, Paper, Scissors game—each strategy may produce a winner or a loser; winning is attributed to luck or perhaps the ability of one player to identify a pattern in the strategies selected by other players. Players in simultaneous move games are well advised to mix their strategies because becoming predictable (always throwing “scissors,” for example) allows the opponent to consistently win. The classic example of a simultaneous move game is represented by what is referred to as the Prisoners’ Dilemma. In this case, a pair of suspected crimi-nals—let’s call them Spencer and Reid—are separated by the police and ques-tioned. Each is individually given the opportunity to confess or to profess in-nocence. The payoff—the number of years’ time to be served—associated with each choice is dependent on the simultaneous decision of that individual’s partner in crime.
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